Projectile Motion

For Projectile Motion, consider an object that is launched with an initial velocity of [math]v_0[/math] at an angle of [math]\theta[/math]. We can think of this as a vector and break it into the horizontal and vertical components.[br]The horizontal velocity will start as [math]v_0\cos\theta[/math]. Gravity does not affect the horizontal velocity, which means that the horizontal displacement will be:[br] [math]x_t=\left(v_0\cos\theta\right)t[/math][br][br]The vertical velocity will start as [math]v_0\sin\theta[/math], but gravity does affect this. From Physics, you can recall that the vertical displacement can be found using [math]d=v_0t+\frac{1}{2}at^2[/math], where [math]a[/math] is acceleration, which we can call [math]g[/math] for acceleration due to gravity. Also, our object may not start at the ground level, so we can adjust the vertical displacement by adding the initial height, [math]h[/math]:[br][math]y_t=\left(v_0\sin\theta\right)t+\frac{1}{2}gt^2+h[/math][br][br]So we have a pair of parametric equations:[br][math]x_t=\left(v_0\cos\theta\right)t[/math][br][math]y_t=\left(v_0\sin\theta\right)t+\frac{1}{2}gt^2+h[/math][br][br]If we are using metric units, [math]g\approx-9.8\frac{m}{s^2}[/math], in standard units, [math]g\approx-32\frac{ft}{s^2}[/math][br][br]Try changing the initial velocity and angle to see how the graph will change. You can zoom and move the graph as needed to see the details.

Information: Projectile Motion